# If a relation R on the set (1,2,3) be defined by R={(1,2)}, then R is

\begin{array}{1 1}(A)\quad reflexive & (B)\quad transitive\\(C)\quad symmetric & (D)\quad none\;of\;these\end{array}

## 1 Answer

Toolbox:
• A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
• A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
• A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
$A=\{1,2,3\}$
$R=\{(1,2)\}$
Since $(1,1)(2,2)(3,3) \notin R$
R is not reflexive
$(1,2) \in R$ but $(2,1) \notin R$
R is not symmetric
$(1,2) \in R$ but $(2,1) \notin R$ and $(1,1) \notin R$
Therefore r is not transitive
Solution:Therefore 'D'option is correct

answered Mar 5, 2013 by
edited Mar 27, 2013 by meena.p

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